was first proposed by [1]} as a part of a class of
estimators collectively called locally adaptive regression
splines. Thus, in the univariate case, \(\hat{f}_{n, V}^1\)  is a
constrained analogue of the locally adaptive regression spline
estimator of [1]} when the order \(k\)  (in the
notation of [1]}) equals
2. [4]} used the terminology
second-order total variation regularization, and
[5]} and [6]} used the
terminology trend filtering for (REF ). For
\(d \ge 1\) , our estimator \(\hat{f}_{n, V}^d\)  is thus
a multivariate generalization of second-order total variation
regularization or trend filtering.
